Probability distribution functions for the masses of the BH and star (m_BH and m_⋆, respectively) and orbital parameters (period P and eccentricity e) for all the detached S–BH binaries in the cluster simulations of Kremer et al. (2020). For ejected binaries, we show their parameters at the time of ejection. The contribution of each binary to the histogram is weighted as explained in Sect. 2. Shown in red (continuous line for 1D histograms, star symbol for 2D histograms) are the values for Gaia BH3. The dashed red line gives the range for the analysis of Gaia BH3-like binaries in Sect. 3. The green lines in the 1D histogram include only the S–BH binaries that were not ejected from their parent cluster.